In this paper, a simple and efficient numerical method for solution of the dynamic interaction of a Shinkansen train (high-speed train in Japan) and the railway structure including post-derailment during an earthquake is given. The motion of the train is modeled using multibody dynamics where nonlinear springs and dampers are used to express the actual dynamic behavior between components in the train [1].

Efficient mechanical models to express contact-impact behavior between wheel and rail in the pre-derailment [2] and between the wheel and track structure with guards attached to prevent the train deviating from the track in the post-derailment during an earthquake are given. Track components such as rail and sleeper with guards attached are modeled with the rail and track elements developed here, where in-plane motions of the cross section of the track components are expressed using multibody dynamics and out-of-plane motions of the cross section in the rail direction are expressed using the finite element method to solve the combined dynamic behavior between a long high-speed train and the long railway structure during an earthquake. A three-dimensional nonlinear spring element based on a trilinear elastic-plastic material model is used for the concrete railway structure as the elastic-plastic behavior appeared in the structure under the cyclic load during an earthquake.

The motion of a railway structure is modeled with various finite elements such as beam, truss, shell, solid, and nonlinear spring and damper elements, and also rail and track elements. The acceleration wave of an earthquake is given at base nodes of the railway structure. The combined transient dynamic response during an earthquake is obtained by solving the equations of motion for the train and railway structure subjected to the interaction between wheel and rail in the pre-derailment and between wheel and track structure attached with guards in the post-derailment. A modal method has been applied to solve large-scale nonlinear equations of motion of the train and railway structure including post-derailment during an earthquake effectively.

Based on the present method a computer program, DIASTARS, has been developed for the simulation of a Shinkansen train running on the railway structure at high speed including post-derailment during an earthquake. Numerical examples are demonstrated.

1

M. Tanabe, S. Komiya, H. Wakui, N. Matsumoto, M. Sogabe, "Simulation and visualization of a high-speed Shinkansen train on the railway structure", Japan J. Indust. Appl. Math., vol.17, pp. 309-320, 2000.

2

M. Tanabe, N. Matsumoto, H. Wakui, M. Sogabe, Y. Tanabe, "An efficient numerical method for dynamic interction analysis of Shinkansen train and railway structure during an earthquake", Proceedings of the 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Las Vegas, Nevada, USA, 2007. doi:10.1115/DETC2007-34475

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